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                                <h2>
                                    1.3 逻辑运算
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                                    2023-09-11, 954 words, 4 min read
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                                        <h2 id="一-逻辑函数">一、逻辑函数</h2>
<h4 id="1-逻辑函数的基本形式">1、逻辑函数的基本形式</h4>
<ul>
<li>
<p>与或表达式</p>
</li>
<li>
<p>与非-与非表达式（由与和非构成、最后一层为非）</p>
</li>
<li>
<p>或与表达式</p>
</li>
<li>
<p>或非-或非表达式</p>
</li>
<li>
<p>或与非表达式</p>
</li>
</ul>
<h4 id="2-逻辑函数基本形式的相互转化">2、逻辑函数基本形式的相互转化</h4>
<p>（了解）</p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>F</mi><mo>=</mo><mi>A</mi><mi>B</mi><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mi>C</mi></mrow><annotation encoding="application/x-tex">F=AB+\overline{A}C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em;"></span><span class="mord mathdefault">A</span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.8833300000000001em;vertical-align:0em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span></span></span></span></p>
<p>1、与或表达式转与非-与非表达式</p>
<p>利用与或式两次取反，再利用摩根定律展开一层</p>
<img src="http://cos.pansis.site/202309150746303.png" alt="image-20230915074607240" style="zoom:33%;" />
<p>2、与或表达式转与或非表达式</p>
<p>先求出反函数的与或式，然后再取反一次</p>
<figure data-type="image" tabindex="1"><img src="http://cos.pansis.site/202309150747322.png" alt="image-20230915074722271" loading="lazy"></figure>
<p>3、与或表达式转或与表达式</p>
<p>将与或非式利用摩根定律展开两层</p>
<img src="http://cos.pansis.site/202309150748830.png" alt="image-20230915074819741" style="zoom:50%;" />
<p>4、或非-或非表达式</p>
<p>或与式两次取反，再利用摩根定律展开一层</p>
<img src="http://cos.pansis.site/202309150749337.png" alt="image-20230915074923263" style="zoom:50%;" />
<figure data-type="image" tabindex="2"><img src="http://cos.pansis.site/202309150750427.png" alt="image-20230915075054059" loading="lazy"></figure>
<h4 id="3-与或式特殊表达形式">3、与或式特殊表达形式</h4>
<figure data-type="image" tabindex="3"><img src="http://cos.pansis.site/202309151428526.png/abc123" alt="image-20230915142824439" loading="lazy"></figure>
<h2 id="二-逻辑函数的表示">二、逻辑函数的表示</h2>
<ul>
<li>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">n</span></span></span></span>个输入，共有<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mn>2</mn><msup><mn>2</mn><mi>n</mi></msup></msup></mrow><annotation encoding="application/x-tex">2^{2^n}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.87998em;vertical-align:0em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.87998em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7385428571428572em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>种逻辑函数式</p>
</li>
<li>
<p>级数：逻辑电路中，输入信号到输出信号所经过的最多的门的个数。</p>
</li>
</ul>
<h4 id="1-方式">1、方式</h4>
<p>逻辑函数式、逻辑图、真值表、卡诺图、波形图（时序图）</p>
<img src="http://cos.pansis.site/202309150752043.png" alt="image-20230915075254702" style="zoom:50%;" />
<h4 id="2-逻辑函数式">2、逻辑函数式</h4>
<p>特别的表示方法</p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>Y</mi><mn>1</mn></msub><mo>(</mo><mi>A</mi><mo separator="true">,</mo><mi>B</mi><mo separator="true">,</mo><mi>C</mi><mo>)</mo><mo>=</mo><mo>∑</mo><mrow><mi>m</mi><mo>(</mo><mn>0</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>4</mn><mo>)</mo><mo>+</mo><mi>d</mi><mo>(</mo><mn>5</mn><mo separator="true">,</mo><mn>6</mn><mo>)</mo></mrow></mrow><annotation encoding="application/x-tex">Y_1(A,B,C)=\sum {m(0,2,4)+d(5,6)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.00001em;vertical-align:-0.25001em;"></span><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault">m</span><span class="mopen">(</span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">4</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">d</span><span class="mopen">(</span><span class="mord">5</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">6</span><span class="mclose">)</span></span></span></span></span></p>
<p>其中<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>m</mi><mo>(</mo><mn>0</mn><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>4</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">m(0,1,2,4)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault">m</span><span class="mopen">(</span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">4</span><span class="mclose">)</span></span></span></span>对应<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo separator="true">⋅</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover><mo separator="true">⋅</mo><mover accent="true"><mi>C</mi><mo stretchy="true">‾</mo></mover><mo separator="true">⋅</mo><mover accent="true"><mi>D</mi><mo stretchy="true">‾</mo></mover><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo separator="true">⋅</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover><mo separator="true">⋅</mo><mi>C</mi><mo separator="true">⋅</mo><mover accent="true"><mi>D</mi><mo stretchy="true">‾</mo></mover><mo>+</mo><mi>A</mi><mi>B</mi><mi>C</mi><mi>D</mi></mrow><annotation encoding="application/x-tex">\overline{A}· \overline{B}·\overline{C}· \overline{D}+\overline{A}· \overline{B}·C· \overline{D}+ABCD</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9666600000000001em;vertical-align:-0.08333em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.9666600000000001em;vertical-align:-0.08333em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault">A</span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span></span></span></span>,</p>
<p>$ d(5,6)$ 为约束条件，代表<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo separator="true">⋅</mo><mi>B</mi><mo separator="true">⋅</mo><mover accent="true"><mi>C</mi><mo stretchy="true">‾</mo></mover><mo separator="true">⋅</mo><mi>D</mi><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo separator="true">⋅</mo><mi>B</mi><mo separator="true">⋅</mo><mi>C</mi><mo separator="true">⋅</mo><mover accent="true"><mi>D</mi><mo stretchy="true">‾</mo></mover><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\overline{A}· B·\overline{C}· D+\overline{A}· B·C· \overline{D}=0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9666600000000001em;vertical-align:-0.08333em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.8833300000000001em;vertical-align:0em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span></p>
<h4 id="2-公式法化简">2、公式法化简</h4>
<p>1、目标：将逻辑函数变成最简与或式，再由与或式转成其他形式。</p>
<p>2、化简原则</p>
<ul>
<li>逻辑电路所用的门最少</li>
<li>每个门的输入端要少</li>
<li>逻辑电路所用的级数要少</li>
<li>逻辑电路能可靠地工作</li>
</ul>
<p>3、与或式化简技巧</p>
<ul>
<li>如果待化简的与或表达式中存在单因子项，且后续与项包含该单因子项或者包含该单因子项的非因子，则 表达式可以得到迅速化简</li>
</ul>
<p>​     <img src="http://cos.pansis.site/202309151013704.png" alt="image-20230915101350616" style="zoom:33%;" /></p>
<ul>
<li>表达式结构与或式中有三项，其中在两项中，某个因子以原变量和 反变量形式分别出现，这两项中其余因子共同构成第三个与项，则 该第三项为多余项，可消去，如果第三项中还包括其他因子，则该 项仍为多余项，可消去</li>
</ul>
<figure data-type="image" tabindex="4"><img src="http://cos.pansis.site/202309151020016.png" alt="image-20230915102018965" loading="lazy"></figure>
<ul>
<li>
<p>其他技巧</p>
<img src="http://cos.pansis.site/202309151020966.png" alt="image-20230915102043920" style="zoom:33%;" />
</li>
</ul>
<h4 id="3-图形法化简卡诺图化简">3、图形法化简（卡诺图化简）</h4>
<p>1、最小项：在与或式中，每个与项包含所有变量，而且在该项中每个变量只能出现一次。</p>
<p>2、<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">n</span></span></span></span>变量逻辑函数共有<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mn>2</mn><mi>n</mi></msup></mrow><annotation encoding="application/x-tex">2^n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.664392em;vertical-align:0em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span></span></span></span></span></span></span>个最小项。</p>
<p>3、最小项性质</p>
<ul>
<li>在输入变量的任一组取值下，有且仅有一个最小项的值为1</li>
<li>一个逻辑函数的任意两个最小项之积必为0</li>
<li>一个逻辑函数的全体最小项之和必为1</li>
</ul>
<p>4、最大项：在或与式中，每个或项包含所有变量，且在该项中每个变量只能出现一次。</p>
<p>5、最大项性质</p>
<img src="http://cos.pansis.site/202309151028310.png" alt="image-20230915102802261" style="zoom:33%;" />
<p>6、卡诺图</p>
<p>略</p>
<p>7、<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>5</mn><mo>≤</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">5\leq n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78041em;vertical-align:-0.13597em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">n</span></span></span></span>变量的卡诺图画法</p>
<p>可由n－1变量卡诺图在需要增加变量 的方向采用镜像变换而生成</p>
<img src="http://cos.pansis.site/202309151029766.png" alt="image-20230915102933694" style="zoom:33%;" />
<p>8、逻辑相邻项</p>
<p>指两个最小项,只有一个变量的形式不同,其余 的都相同,并且逻辑相邻的最小项可以合并。</p>
<img src="http://cos.pansis.site/202309151030992.png" alt="image-20230915103025946" style="zoom:50%;" />
<p>9、卡诺图上的最小项合并</p>
<img src="http://cos.pansis.site/202309151032563.png" alt="image-20230915103247507" style="zoom:50%;" />
<figure data-type="image" tabindex="5"><img src="http://cos.pansis.site/202309151033808.png" alt="image-20230915103304750" loading="lazy"></figure>
<img src="http://cos.pansis.site/202309151033487.png" alt="image-20230915103314416" style="zoom:50%;" />
<h4 id="4-带约束条件的化简">4、带约束条件的化简</h4>
<p>方法：卡诺图</p>
<p>约束条件画×，在卡诺图中可圈可不圈。</p>
<img src="http://cos.pansis.site/202309221504571.jpg/abc123" alt="b1b49cafbebd6110792f47a9eaeb0a4" style="zoom: 50%;" />
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